Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2412.02103 |
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Inhaltsangabe:
- We study the dynamics of the focusing nonlinear Hartree equation with a Kato potential $$ i\partial_t u +Δu - Vu = -(|\cdot|^{-γ} \ast |u|^2)u, \quad x \in \mathbb{R}^d $$ under some assumptions on the potential $V$. We prove the blow up versus global existence dichotomy for solutions beyond the threshold, based on the method from Duyckaerts-Roudenko [6]. Furthermore, our result compensates for the one of in [13] below that threshold.